Abstract In this paper, the stability problem is investigated for networked control systems. Input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols are considered. A unified framework based on the hybrid systems with memory is proposed to model the whole networked control system. Hybrid systems with memory are used to model hybrid systems affected by delays and permit multiple jumps at a jumping instant. The stability analysis depends on the Lyapunov–Krasovskii functional approaches for hybrid systems with memory and the proposed stability theorem does not need strict decrease of the Lyapunov–Krasovskii functional during jumps. Based on the developed stability theorems, stability conditions for networked control systems are established. An explicit formula is given to compute the maximal allowable transmission interval. In the special case that the networked control system contains linear dynamics, an explicit Lyapunov functional is constructed and stability conditions in terms of linear matrix inequalities (LMI) are proposed. Finally, an example of a chemical batch reactor is given to illustrate the effectiveness of the proposed results.

中文翻译：

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具有采样、传输协议和输入延迟的网络控制系统的稳定性分析

摘要 本文研究了网络控制系统的稳定性问题。考虑了输入延迟和包含时变传输间隔和传输协议的多重通信缺陷。提出了一个基于带记忆混合系统的统一框架来对整个网络控制系统进行建模。具有内存的混合系统用于模拟受延迟影响的混合系统，并允许在跳跃瞬间进行多次跳跃。稳定性分析依赖于具有记忆的混合系统的 Lyapunov-Krasovskii 泛函方法，并且所提出的稳定性定理不需要在跳跃期间严格减少 Lyapunov-Krasovskii 泛函。基于所发展的稳定性定理，建立了网络控制系统的稳定性条件。给出了一个明确的公式来计算最大允许传输间隔。在网络控制系统包含线性动力学的特殊情况下，构建了一个显式的Lyapunov泛函，并提出了线性矩阵不等式（LMI）的稳定性条件。最后，给出了一个化学间歇反应器的例子来说明所提出结果的有效性。